河北省(衡水金卷)普通高等学校2016届高三全国招生统一模拟考试(全国卷I)理数试题(五)Word版含答案.doc
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2016年普通高等学校招生全国统一考试模拟试题语文(一)注意事项:1.本试卷分第I卷(阅读题)和第Ⅱ卷(表达题)两部分,答卷前,考生务必将自己的姓名、准考证号填写在答题卡上2.作答时,请认真阅读答题卡上的注意事项,将答案写在答题卡上。
写在本试卷上无效3.考试结束后,将本试卷和答题卡一并交回第I卷阅读题甲必考题一、现代文阅读(9分,每小题3分)阅读下面的文字,完成l~3题。
百年中国,再没有其他学说像儒家思想这样,经历了如此长时间的反复跌宕和严峻拷问。
读经和反对读经,曾成为学界和舆论界争吵不休的一桩公案。
反对者显然占上风,连鲁迅也站出来发声,批评提倡读经者即使是真正的老实人也不过是“笨牛”而已。
文革十年,儒家思想成为众矢之的,必欲清除扫尽而快之。
改革开放后,把历史还给历史成为思想学术界共同呼声,孔子由被幼童也参与唾骂的斯文扫地变而为正常的文化古人。
由于所经历的“毁圣弃知”的时间实在太长,难免积非成是,改变世人乃至学界部分人士的成见尚需时日。
儒学产生之初,即春秋战国时期,儒家只是诸子百家中的一家,其影响比之墨家或犹有未及。
所以孟子颇为焦虑地说:“圣王不作,诸侯放恣,处士横议,杨朱、墨翟之言盈天下。
天下之言不归杨,则归墨。
”他因此想起而矫正此种“仁义充塞”的时代风气,欲以承继虞舜、周公、孔子的圣道为己任。
汉代中期汉武帝实施“独尊儒术,罢黜百家”的政策,使儒学地位骤然提升,成为社会主流意识形态。
但儒学以外的学说仍有存在空间。
东汉佛教的传入和道教的兴起,即为明证。
而到魏晋南北朝时期,释、道、玄之风大炽,其思想所宗更非只有儒学一家。
隋唐佛教发展的势头,亦不在儒学之下。
但如果认为隋唐时期的思想主潮是佛而非儒,轻忽儒家地位,又有误读古人之嫌。
直承郑康成而撰《五经正义》的孔颖达,即是当时继往开来的儒学健将。
明清以还,儒学的地位日趋稳固,但佛、道两家在民间社会的影响也开始定式成型儒家思想在宋代呈现变易之势。
二程和朱子等宋代大儒,诚然是承继了先秦以孔子、孟子为代表的儒家思想,但朱子的理学实为思想大汇流的产物,道家和道教的思想,佛教特别是禅宗的思想,一起参与进来成为理学的助发资源。
2016高考置换卷一一、选择题(本大题共21个小题,每小题6分,共126分。
1-18小题单选,19-21小题多选。
)1.下列有关细胞分子组成及结构的描述,正确的是()A.D NA、tRNA、rRNA、mRNA都参与了细胞中蛋白质的合成B.单体都不具备物种特异性,而多聚体都有物种特异性C.内质网与蛋白质、脂质、糖类的合成都有关,因此被称为“养料制造厂”D.有氧呼吸及光合作用产生的ATP均在膜上完成2.下列关于植物生长素及其类似物的叙述,不正确的是()A.同一种植物的幼芽对生长素的反应敏感程度高于幼根B.棉花表现出的顶端优势与顶芽产生的生长素的极性运输有关C.在番茄花期喷洒一定浓度的2,4—D可防止落花落果D.用一定浓度的IBA溶液浸泡葡萄插条基部可诱导生根3.长时间行走使脚掌磨出了水泡,几天后水泡消失。
此时水泡中的液体主要渗入()A.组织细胞 B.毛细血管和各级动脉、静脉C.各级动脉和静脉 D.毛细血管和毛细淋巴管4.下列关于群落及其演替的说法不正确的是()A.如果时间允许,弃耕的农田一定能形成森林B.演替过程中,因灌木较为高大而取代草本植物C.群落演替是一个群落代替另一个群落的过程D.人类的活动会影响群落演替的方向和速度5.下列关于遗传信息的相关图形,描述正确的是()A.人体成熟红细胞属于高度分化的细胞不能进行①过程,但可以进行②③过程B.①过程和②过程用到的酶分别是DNA聚合酶和RNA聚合酶C.③所示过程可发生在蓝藻细胞内,核糖体移动方向从左至右D.据②原理可制成DNA探针,用于检测目的基因在受体细胞中是否成功表达6.绿色荧光标记的X染色体DNA探针(X探针),仅能与细胞内的X染色体DNA的一段特定序列杂交,并使该处呈现绿色荧光亮点。
同理,红色荧光标记的Y染色体DNA探针(Y探针)可使Y染色体呈现一个红色荧光亮点。
同时用这两种探针检测体细胞,可诊断性染色体数目是否存在异常。
医院对某夫妇及其流产胎儿的体细胞进行检测,结果如图所示。
2016年普通高等学校招生全国统—考试模拟试题理科综合能力测试(一)物理试题二、选择题:本题共8小题.每小题6分。
在每小题给出的四个选项中.第14~18题只有一项符合题目要求.第19~21题有多项符合题目要求。
全部选对的得6分。
选对但不 全的得3分。
有选错的得0分。
14.2016年我国将择机发射“天宫二号”空间实验室,以期掌握推进剂的在轨补加技术和解决航天员中期驻留问题。
随后还将发射“神舟十一号”载人飞船和“天舟一号”货运飞船与“天宫二号”空间实验室进行对接,逐步组建我们的空间站。
若发射后的“天宫二号”和“天舟一号”对接前运行的轨道为如图所示的两个圆形轨道,其中“天宫二号”在较高轨道上运行,A 、B 、C 为两轨道同一直线上的三个点,O 点为地心,现让“天舟一号”变轨加速(可简化为一次短时加速)实现二者对接,下列有关描述中正确的是A .“天舟一号”在B 点加速时可在C 点与“天宫二号"实现对接B .“天舟一号”加速后变轨对接过程中的速度一直在增大C .“天舟一号”与“天宫二号”组合体的加速度大于“天舟一号”加速前的加速度D .“天舟一号”与“天宫二号”组合体绕行周期大于“天舟一号”加速前的绕行周期15.如图为某种型号手机充电器的简化电路图,其中副线圈的中心抽头有一根引线,该 装置先将市网电压通过一个小型变压器后,再通过理想二极管D 连接到手机电源上。
已知原副线圈的匝数比为22:1,若原线圈中输入的电压为()2202sin314u t V =,则下列说法正确的是A .手机电源得到的是脉动直流电,其频率为50 HzB .手机电源得到的是正弦交流电.其频率为50 HzC .该装置正常工作时手机电源获得的电压为5 VD .若其中一个二极管烧坏不能通电,另一个还能工作,此时手机电源获得的电压为2.5 V16.自2014年12月份始,我国已有14个省市电子不停车收费系统(简称ETC)正式联网运行,这一系统极大地方便了司机和收费工作人员。
2016年普通高等学校招生全国统一考试模拟试题理科数学(一)注意事项:1.本试卷分第I 卷(选择题)和第Ⅱ卷(非选择题)两部分。
答卷前,考生务必将自己的姓名、准考证号填写在答题卡上。
2.回答第I 卷时,选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动,用橡皮擦干净后,再选涂其它答案标号。
写在本试卷上无效。
3.回答第Ⅱ卷时,将答案写在答题卡上,写在本试卷上无效。
4.考试结束后,将本试卷和答题卡一并交回。
第I 卷一.选择题:本大题共12小题,每小题5分,在每小题给出的四个选项中,只有一项是符合题目要求的。
(1)已知i 是虚数单位,复数11z i i=+-,则复数z 的虚部是 (A) 12-(B) 32 (C) 32- (D)2(2)若集合{}{}222,20x A y y B x x x ==+=-++≥,则 (A) A B ⊆(B) A B R ⋃= (C) {}2A B ⋂= (D A B ⋂=∅(3)已知定义域为[]2,21a a --的奇函数()3sin 1f x x x b =-++,则()()f a f b +的值为 (A)0(B)1(C)2 (D)不能确定(4)已知函数()()1201x f x a a a +=->≠且的图象恒过定点A ,设抛物线24E y x =:上任意一点M 到准线l 的距离为d ,则d MA +的最小值为(A)5(B)(C) (D)(5)执行如图所示的程序框图,其中输入的x i 值依次为14,8,42,78,96,74,49,35,39,50,则输出的i x 值依次为 (A)78,96,74,49,50(B)78,96,74,39,50 (C)78,96,74,50(D)78,96,74(6)下列说法正确的是(A)“a R ∃∈,方程220ax x a -+=有正实根”的否定为“a R ∀∈,方程220ax x a -+=有负实根”(B)命题“a b R ∈、,若220a b +=,则0a b ==”的逆否命题是“a b R ∈、,若0a ≠,且b ≠0,则220a b +≠”(C)命题p :若回归方程为1y x -=,则y 与x 负相关;命题q :数据1,2,3,4的中位数是2或3.则命题p ∨q 为真命题(D)若X ~N(1,4),则()()212P X t P X t <-=>成立的一个充分不必要条件是t =1 (7)等差数列{}n a 中的两项22016a a 、恰好是关于x 的函数()()228f x x x a a R =++∈的两个零点,且100910100a a +>,则使{}n a 的前n 项和n S 取得最小值的行为 (A)1009(B)1010(C)1009,1010D.2016(8)某省巡视组将4名男干部和2名女干部分成两小组,深入到A 、B 两城市进行巡视工作,若要求每组最多4人,且女干部不能单独成组,则不同的选派方案共有 (A)40种(B)48种 (C)60种(D)72种(9)某几何体的三视图如图所示,其中正视图和侧视图是全等的等腰三角形,现从该几何体的实心外接球中挖去该几何体,则剩余几何体的体积是(A)9146π- (B)91162π- (C) 91166π- (D)9186π-(10)已知函数()()2sin 0y x ωϕω=+>的部分图象如图所示,点,06A B C π⎛⎫- ⎪⎝⎭、、是该图象与x 轴的交点,过点B 作直线交该图象于D 、E 两点,点7012F π⎛⎫⎪⎝⎭,是()f x 的图象的最高点在x 轴上的射影,则()()AD EA AC ω-的值是(A) 22π (B) 2π(C)2(D)以上答案均不正确(11)已知点12F F 、是双曲线()222210,0x y C a b a b-=>>:的左、右焦点,O 为坐标原点,点P 在双曲线C 的右支上,且满足12122,3F F OP PF PF =≥,则双曲线C 的离心率的取值范围为 (A )()1,+∞(B )102⎫+∞⎪⎪⎣⎭(C )101,2⎛ ⎝⎦(D )51,2⎛⎤ ⎥⎝⎦(12)已知定义在R 内的函数()f x 满足()()4f x f x +=,当[]1,3x ∈-时,()f x =()[](]1,1,1,,1,3,t x x x ⎧-∈-⎪∈则当8,27t ⎛⎤∈ ⎥⎝⎦时,方程()720f x x -=的不等实数根的个数是(A)3(B)4(C)5(D)6第Ⅱ卷本卷包括必考题和选考题两部分。
数学(文)试题(五)第Ⅰ卷(共60分)一、选择题:本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的.1. 已知集合(){}(){},|1,,|42A x y y x B x y y x ==+==-,则A B = ( )A .(){}1,2 B .()1,2 C .{}1,2 D .()(){}1,2,1,2--2. 已知复数1(12iz i i +=+为虚数单位), 则( ) A .z 的实部为15- B .z 的虚部为15i -C .35z =D .z 的共轭复数为3155i +3. 焦点在y 轴上的椭圆()222:106x y C a a +=>,则实数a 为( ) A .3 B .2 C .2或3 D .4或94. 执行如图所示的程序框图, 则输出的结果是( )A .1B .43 C .54D .2 5. 如图所示, 一报刊亭根据某报纸以往的销售记录, 绘制了日销售量的频率分布直方图, 但原始数据遗失, 则对日销售量中位数的估计值较为合理的是( )A .100B .113C .117D .125 6. 已知1sin 24πα⎛⎫+=⎪⎝⎭,则cos 2α=( )A .78-B .78C .78或78- D7. 已知双曲线 ()2222:10,0x y C a b a b -=>>的虚轴端点到一条渐近线的距离为2b,则双曲线C 渐近线方程为( )A .y =B .2y x =C .y =D .y = 8. 已知函数()()()ln 01x f x a b a a =+>≠且是R 上的奇函数, 则不等式()ln f x a a >的解集是( ) A .(),a +∞ B .(),a -∞C .当1a >时, 解集是(),a +∞;当01a <<时, 解集是(),a -∞D .当1a >时,解集是(),a -∞;当01a <<时, 解集是(),a +∞9. 一个几何体的三视图如图所示, 其中府视图与侧视图均为半径是1的圆, 则这个几何体的体积是( )A .3πB .23π C .π D .43π10. 将函数()()sin 206f x x πωω⎛⎫=+> ⎪⎝⎭的图象上所有点的横坐标变为原来的2倍, 纵坐标不变, 再将其向左平移6π个单位后, 所得的图象关于y 轴对称, 则ω的值可能是( )A .12 B .32C .5D .2 11. 在等比数列{}n a 中, 若25234535,44a a a a a a =-+++=,则23451111a a a a +++=( ) A .1 B .34-C .53-D .43- 12. 已知函数()()()()()1log 111,0,12113a x x f x a a f x a x ⎧⎛⎫-<<⎪ ⎪+=>≠⎝⎭⎨⎪--+<<⎩, 若12x x ≠,则()()12f x f x =时,12x x + 与2的大小关系是( )A .恒小于2B .恒大于2C .恒等于2D .与a 相关第Ⅱ卷(共90分)二、填空题(每题5分,满分20分,将答案填在答题纸上)13. 已知向量()()()1,3,2,0,2,a b c k =-==- ,若()()2a b c -⊥-,则k = .14. 设变量,x y 满足不等式组403301x y x y x +-≤⎧⎪-+≤⎨⎪≥⎩,若4z x y =--,则z 的取值范围是 .15. 某工厂实施煤改电工程防治雾霾, 欲拆除高为AB 的烟囱, 测绘人员取与烟囱底部B 在同一水平面内的两个观测点,C D ,测得75,60,40BCD BDC CD ∠=∠==米, 并在C 处的正上方E 处观测顶部A 的仰角为30 ,且1CE =米, 则烟囱高AB = 米.16. 已知函数()f x 是周期为2的偶函数, 且当[]0,1x ∈时,()2f x x =, 函数()()0g x kx k =>,若不等式()()f x g x ≤的解集是[][][)()0,,,0a b c d d c b a +∞>>>> ,则正数k 的取值范围是 .三、解答题 (本大题共6小题,共70分.解答应写出文字说明、证明过程或演算步骤.)17. (本小题满分12分)已知数列{}n a 的前n 项和为n S ,且()ln 1n S n =+. (1)求数列{}n a 的通项公式;(2)设(na nb e e =为自然对数的底数), 定义:1231...nkn k bb b b b ==∏ ,求1nk k b =∏.18. (本小题满分12分)如图1,在直角梯形ABCD 中, ,AB CD AB AD ⊥ ,且1,2,3,,AE AB CD E F ===分别为,AB CD 上的点, 以EF 为轴将正方形ADFE 向上翻折, 使平面ADFE 与平面BEFC 垂直如图2.(1)求证:平面BDF ⊥平面BCD ; (2)求多面体AEBDFC 的体积.19. (本小题满分12分)随机抽取某中学高三年级甲, 乙两班各10名同学, 测量出他们的身高(单位:cm ),获得身高数据的茎叶图, 其中甲, 乙两班各有一个数据被污损.(1)若已知甲班同学身高众数有且仅有一个为179,乙班同学身高的中位数为172,求甲, 乙两班污损处的数据;(2)在(1) 的条件下, 求甲, 乙两班同学身高的平均值;(3) ①若已知甲班同学身高的平均值大于乙班同学身高的平均值, 求甲班污损处的数据的值;②在①的条件下, 从乙班这10名同学中随机抽取两名身高高于170cm 的同学, 求身高为181cm 的同学被抽中的概率.20. (本小题满分12分)已知抛物线2:4C y x =的焦点为F ,过点()2,0P 的直线交抛物线于,A B 两点.(1)若11FA FB =-,求直线AB 的方程;(2)求ABF ∆面积的最小值.21. (本小题满分12分)设函数()ln 1nf x x m x =--,其中,2,0n N n m *∈≥≠.(1)当2n =时, 求函数()f x 的单调区间; (2)当1m =时, 讨论函数()f x 的零点情况.请考生在22、23、24三题中任选一题作答,如果多做,则按所做的第一题记分.22.(本小题满分10分)选修4-1:几何证明选讲如图, 已知圆上的四点A 、B 、C 、,D CD AB ,过点D 的圆的切线DE 与BA 的延长线交于E 点. (1)求证:CDA EDB ∠=∠;(2)若5,7BC CD DE ===,求线段DE 的长.23. (本小题满分10分)选修4-4:坐标系与参数方程在直角坐标系xOy 中, 以O 为极点,x 轴正半轴为极轴建立极坐标系, 圆C 的极坐标方程为2cos ρθ=,直线l 的参数方程为2(12x t t y t =⎧⎪⎨=+⎪⎩为参数), 直线l 和圆C 交于,A B 两点,P 是圆C 上不同于,A B 的任意一点.(1)求圆心的极坐标;(2)求点P 到直线l 的距离的最大值.24. (本小题满分10分)选修4-5:不等式选讲 设函数()()820f x x x m m m=++-> . (1)求函数()f x 的最小值;(2)求使得不等式()110f >成立的实数m 的取值范围.2016年(衡水金卷)普通高等学校招生全国统一模拟考试(全国卷I )数学(文)试题(五)参考答案一、选择题(每小题5分,共60分)1-5.ADBAC 6-10.ADCCD 11-12.CB 二、填空题(每小题5分,共20分) 13.23 14.7,62⎡⎤⎢⎥⎣⎦15.1+ 16.11,53⎡⎫⎪⎢⎣⎭三、解答题17.解:(1)当1n =时,11ln 2a S == ;当2n ≥且n N *∈18. 解:(1)由题可知,2,FB BC FC BC BF ===∴⊥.又DF EF ⊥ ,平面ADFE ⊥平面,BEFC DF ∴⊥平面,,BEFC DF BC BC ∴⊥∴⊥平面,BDF ∴平面BDF ⊥平面BCD .(2)多面体AEBDFC 可分为四棱锥B AEFD -和三棱锥B DFC -,11,33B AEFD AEFD V S EB -== 四棱锥正方图FC 111323B D V DF FC EF -=⨯= 三棱锥,则多面体AEBDFC 的体积为23.19. 解:(1)因为已知甲班同学身高众数有且仅有一个为179,所以甲班污损处是9 . 因为乙班同学身高的中位数为172,所以乙班污损处是4.(2)由(1) 得甲班同学身高的平均值为158162163168168171179179179182170.910+++++++++=,乙班同学身高的平均值为159162165168170174176178179181171.210+++++++++=.(3) ①设甲, 乙班污损处的数据分别为(),09,09,,x y x y x y N ≤≤≤≤∈,则甲班同学身高的平均值为()158162...170 (1821701010)x x++++++=+,乙班同学身高的平均值为()159162...170...17918181701010y y ++++++++=+,由题意,81701701010x y ++>+. 解得8x y >+.又09,09,,x y x y N ≤≤≤≤∈,则min 0y =,得8,9x x >∴=,此时0y =. 故甲班污损处的数据的值为9.②设“身高为181cm 的同学被抽中” 为事件A ,从乙班10名同学中抽取两名身高高于170cm 的同学有:{}{}{}{}{}{}176,178,176,179,176,181,178,179,178,181,179,181共6个基本事件, 而事件A 含有{}{}{}176,181,178,181,179,181共3个基本事件, 所以()3162P A ==. 20. 解:(1)不妨设点A 在x 轴上方,①当直线AB 的斜率不存在时, 直线方程为2x =,此时将2x =代入抛物线2:4C y x =中, 得28y =,解得y =±所以点,A B的坐标分别为((2,,2,-,又焦点F 的坐标为()1,0,则((1,,1,FA FB ==-,所以((1,1,187FA FB =-=-=- ,不满足11FA FB =-,故舍去;②当直线AB 的斜率存在时, 设斜率为k 显然0k ≠,故直线AB 方程为()2y k x =-.设点()()()112212,,,0,0A x y B x y y y ><,联立()224y k x y x ⎧=-⎪⎨=⎪⎩,消去y ,得()22224440k x k x k -++=,且232160k ∆=+>,则由韦达定理,得(2121212244,4,k x x x x y y k ++==∴=-8=-=-,又焦点F 的坐标为()1,0, 所以()()()()1212111212121211,1,1FA FB x x y y x y x x x x x x y y =+++=--=+-++++()2224444187k k k +=-++-=--.由题意,24711k--=-, 解得1k =±, 所以直线AB 方程为2y x =-或2y x =-+,即20x y --=或20x y +-=.(2)①当直线AB 的斜率不存在时, 由(1)得, 点,A B的坐标分别为((2,,2,-,所以ABF ∆的面积为(1211122S PF y y y =⨯⨯-=-- ②当直线AB 的斜率存在时, 设斜率为k 显然0k ≠,由(1) 得,21212244,4k x x x x k++==, 所以ABF ∆的面积为1211122S PF y y y =⨯⨯-=-====>=. 综上所述,ABF ∆ 面积的最小值为21. 解:(1)依题意得,()()()222ln 1,0,,'2m x m f x x m x x f x x x x-=--∈+∞∴=-=, 当0m <时,()'0f x >, 函数()f x 在区间()0,+∞内单调递增;当0m >时, 令()'0f x >,得x >;令()'0f x <,得0x <<则函数()f x在区间⎛ ⎝内单调递减;在区间⎫+∞⎪⎪⎭内单调递增.(2)依题意得,()()()111ln 1,0,,'n nn nx f x x x x f x nxx x--=--∈+∞∴=-=, 令()0'0f x =得0010,n nx x -==,因为2n ≥,所以函数()f x 在区间()00,x 内单调递减;在区间()0,x +∞内单调递增,所以()()()0min 1111ln 1ln 11ln f x f x n n n n n n n==--=+-=+-,令()()ln 12p x x x x =-+≥,则()()()1'10,2ln 210p x p x p x=-<∴≤=-<,ln 10n n ∴-+<,即()00f x <, ()()012,210x f f =<<∴>= ,又因为0111111,ln 1ln 0nnx n n ne ne ne ne ne ⎛⎫⎛⎫⎛⎫=>>∴=--=+> ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭,根据零点存在性定理知, 函数()f x在⎛ ⎝和⎫⎪⎪⎭+∞内各有一个零点. 22. 解: (1),CD AB BDC ABD ∴∠=∠ ,又由DE 是圆的切线, 知,,ADE ABD ADE BDC CDA EDB ∠=∠∴∠=∠∴∠=∠.(2)在,BCD ADE ∆∆中,,,,,.BC CD AD BDC EDA BCD EAD BDC EDA BC EA ==∠=∠∠=∠∴∆∆≅∆∴= 又由切割线定理得,2DE EA EB = , 即49495,5BE BE =∴=. 23. 解:(1)由2cos ρθ=,得22cos ρρθ=,得222x y x +=,故圆C 的普通方程为2220x y x +-=,所以圆心坐标为()1,0,圆心的极坐标为()1,0.(2)直线l 的参数方程为2(12x tt y t =⎧⎪⎨=+⎪⎩为参数) 化为普通方程是210x y -+=,即直线l 的普通方程为210x y -+=,因为圆心()1,0到直线:210l x y -+=的距离d ,所以点P 到直线l 的距离的最大值1r d +=+=. 24. 解:(1)由0m >,有()()88882222f x x x m x x m m m m m m m=++-≥+--=+=+,当且仅当()820x x m m ⎛⎫+-≤ ⎪⎝⎭时, 取等号, 所以()f x 的最小值为82m m +. (2)()()811210m mf m =++>+,当120m -<,即12m >时,()()8811221m m m f m +--=+=,由()110f >,得8210m m +>,化简得2540m m -+>,解得1m <或4m >,所以112m <<或4m >,当120m -≥,即102m <≤时,()()88111222f m m m m =++-=+-, 由()110f >,得82210m m +->,此式在102m <≤时恒成立, 综上, 当()110f >时, 实的实数m 的取值范围是()()0,14,+∞ .。
2016英语衡水金卷答案【篇一:(衡水万卷)2016年普通高等学校招生全国统一考试模拟英语试题(一)(含答案解析)】ss=txt>第i卷第二部分阅读理解(共两节,满分40分)第一节(共15题;每题2分,满分30分)阅读下列短文,从每题所给的四个选项(a、b、c和d)中,选出最佳选项。
athis story took place a long time ago. but it has been repeated time and time again. everyone is moved by the true story.an old man was knocked down by a car and was taken to hospital. he was badly hurt, and during his few returns to consciousness, he repeatedly called for his son.none knew where his son was. a dirty letter was found in his pockets. the nurse learned that his son was a solider in north carolina.the hospital called the red cross offices to find the young man. the young solider was rushed to the airport in time to catch the plane.it was evening when the young solider walked into the hospital. a nurse took him into the bedsides of the old man.―your son is here,‖ she said to the man. she had to repeat the words several times before the old man’s eyes opened. he dimly saw the young man and got great comfort. he reached out his hand. the young solider held the old man’s hand and offered words of hope.all through the night the young solider sat besides the bed. the nurse offered to watch instead of him for a while. he refused.at dawn the old man died. the nurse started to comfort him but the solider asked her, ―who was that old man?‖―he was your father,‖ she answered.―no, he wasn’t. i never saw him before.‖―i knew right away there was a mistake, but i also knew he needed his son, and his son just wasn’t here. i realized i was needed. so i stayed.‖21. what is true about the old man?a. he was seriously injured and would die soon.b. he knew quite well what had happened to him.c. he once and again wanted to call his son.d. he was knocked dead near a hospital.22. how did people get to know something about his son?a. they guessed from the old man’s anxious expression on the face.b. they found him from the address on the letter.c. they found someone who knew the father and son.d. they asked for the help from the red cross.23. when the old man and the young man met, ________. a. the old man wished the young man good luck in the future b. the young man said something to comfort the old man c. the doctors and nurses felt it hopeful to save the old man d. they both recognized each other at once 24. we know from this passage________.a. the red cross is something for people to find personsb. the young man knew he was wrongly called when he got on the planec. the hospital had meant to save the old man with the young man’s coming but failedd. the young man might have the same name as the old man’s sonchief executive office lahore stock exchangelahore stock exchange(lse) is the 2nd largest exchange of the country with a workforce of almost 150 employees. the exchanges of pakistan are currently understanding a major reform program involving demutualization(使成为股东制) in order to develop the capital markets further.we seek a dynamic, forward-thinking chief executive with ability to provide strong leadership and effective management to deliver its organizational goals and strategic plan. the successful candidate should have the business both pre and post demutualization with a proven record.the candidate should have minimum of 7 years of experience along with a business related degree or other professional qualifications. however, a strong record of achievement, excellent communication and team beam building skill are equally important. international qualifications/experience will be an added advantage together with the knowledge of the local corporate environment.and be part of an organization to make a difference, please write to:head of human resources, lahore stock exchange(guarantee) ltd. 19 knayaban-e-aiwan-iqbal, lahore, pakistan, together with your curriculum vitae and latest passport sized photograph.25. what is not true about lse? a. it’s lahore stock exchange.b. it’s one of the largest exchanges in pakistan.c. it’s developing pakistan’s capital city.d. it’s located in knayban-e-aiwan–iqbal, lahore, pakistan. 26. what is wanted according to this advertisement?a. lahore stock exchangeb. a chief executivec. head of human resourcesd. a candidate27. what does the underlined word compensation probably mean? a. salary b. job c. working conditions d. foodcmedia selection for advertisementsafter determining the target audience for a product or service, advertising agencies must select the appropriate media for the advertisement. we discuss here the major types of media used in advertising. we focus our attention on seven types of advertising: television, newspapers, radio, magazines, out-of-home. internet, and direct mail.televisiontelevision is an attractive medium for advertising because it delivers mass audiences to advertisers. when you consider that nearly three out of four americans have seen the game show who wants to be a millionaire? you can understand the power of television to communicate with a large audience. when advertisers create a brand, for example, they want to impress consumers with the brand and its image. television provides an ideal vehicle for this type of communication.but television is an expensive medium, and not all advertisers can afford to use it.televisions influence on advertising is fourfold. first, narrowcasting means that television channels are seen by an increasingly narrow segment of the audience. the golf channel, for instance.is watched by people who play golf. home and garden television is seen by those interested in household improvement projects. thus, audiences are smaller and more homogeneous(具有共同特点的) than they have been in the past.second, there is an increase in the number of television channels available to viewers, and thus, advertisers. this has also resulted in an increase in the sheer number of advertisements to which audiences are exposed. third, digital recording devices allow audience members more control over which commercials they watch. fourth, control over programming is being passed from the networks to local cable operators and satellite programmers.newspaper?after television, the medium attracting the next largest annual ad revenue is newspapers. the new york times, which reaches a national audience, accounts for $1 billion in ad revenue annually, ii m increased its national circulation (发行量) byb40% and is now available for home delivery in ion ciues. locally, newspapers are the largest advertising medium.newspapers are a less expensive advertising medium than television and provide a way for advertisers to communicate a longer. more detailed message to their audience than they can through 48 hours,meaning newspapers are also a quick way of getting the massage out.newspapers are ofen the most important form of news for a local community, and they develop a high degree of loyalty from local reader.radioadvertising on radio continues to grow radio is often used in conjunction with outdoor bill-boards (广告牌) and ihe internetto reach even more customers than television. advertisers are likely to use radio because it is a less expensive medium than television, which means advertisers can afford to repeal their ads often. internet companies are also turning 10 radio advertising. radio provides a way for advertisers to communicate with audience members at all times of theday.consumers listen to radio on their way to school or work,at work, on the way home, and in the evening hours.two major changes—satellite and internet radio—will force radio advertisers to adapt their methods. both of these radio forms allow listeners to tune in stations that are more distant than thelocal stations they could receive in the past. as a result, radio will increasingly attract target audiences who live many miles apart.magazinesnewsweeklies, women’s titles, and business magazines have all seen increases in advertising because they attract the high-end market, magazines are popular with advertisers becauseof the narrow market that they deliver. a broadcast medium such as network television attracts all types of audience members, but magazine audiences are more homogeneous, if you read sports illustrated, for example, you have much in common with the magazine’s other readers. advertisers see magazines as an efficient way of reaching target audience members.advertiser using the print media-magazines and newspapers-will need to adapt to two main changes. first, the internet will bring larger audiences to local newspapers, these second. advertisers will have to understand how to use an increasing number of magazines for their target audiences. althoughsome magazines will maintain national audiences, a large number of magazines will entertain narrower audiences.out-of-home advertisingout-of-home advertising. also called place-based advertising, has become an increasingly effective way of reaching consumers, who are more active than ever before. many consumers today do not sit at home and watch television. using billboards, newsstands, and bus shelters for advertising is an effective way of reaching these on-the-go consumers. more consumers travel longer distances to and from work, which also makes out-of-home advertising effective, technology has changed the nature of the billboard business, making it a more effective medium than in the past.using digital printing, billboard companies can print abillboard in 2 hours, compared with 6 days previously. this allows advertisers more variety in the types of messages they create because they.can change their messages more quickly.internetas consumers become more comfortable with online shopping, advertisers will seek to reach this market as consumers get more of their news and information from the internet, theability of television and radio to get the word out to consumers will decrease. the challenge to internet advertisers is to create ads that audience members remember.internet advertising will play a more prominent role in organizations advertising in the near ftuture. internet audiences tend to be quite homogeneous, but small. advertisers will have to adjust their methods to reach these audiences and will have to adapt their persuasive strategies to the online medium as well.direct maila final advertising medium is direct mail, which uses mailings to consumers to communicate a clients message direct mail includes newsletters. postcards and special promotions. direct mail is an effective way to build relationships with consumers.for many businesses.direct mail is the most effective from of advertising.28. with the increase in the number of tv channels_________. a. the cost of tv advertising has decreased b. the nuiflber of tv viewers has increasedc. advertisers interest in other media has decreasedd. the number of tv ads people can see has increased30.advertising on radio continues to grow because___________. a. more local radio stations have been set up b. modern technology makes it more entertaining c. it provides easy access to consumersd. it has been revolutionized by internet radio.31.magazines are seen by advertisers as an efficient wayto___________. a. reach target audiencesb. modern technology makes it more entertainingc. appeal to educated people.d. convey all kinds of messagesduniversities branch outas never before in their long history, universities have become instruments of national competition as well as instruments of peace. they are the place of the scientific discoveries thatmove economies forward, and the primary means of educating the talent required to obtain and maintain competitive advantage. but at the same time, the opening of national borders to the flow of goods, services, information and especially people has made universities a powerful force for global integration, mutual understanding and geopolitical stability.in response to the same forces that have driven the world economy, universities have become more self-consciouslyglobal: seeking students from around the world who represent the entire range of cultures and values, sending their own students abroad to prepare them for global careers, offering courses of study that address the challenges of an interconnected world and collaborative (合作的) research programs to advance science for the benefit of all humanity.of the forces shaping higher education none is more sweeping than the movement across borders.over the past three decades the number of students leaving home each year to study abroad has grown at an annual rate of 3.9 percent, from 800 000 in 1975 to 2.5 million in 2004. most travel from one developed nation to another, but the flow from developing to developed countries is growing rapidly. the reverse flow, from developed to developing countries, is on the rise, too.today foreign students earn 30 percent of the doctoral degrees awarded in the united states and 38 percent of those in the united kingdom. and the number crossing borders for undergraduate study is growing as well, to 8 percent of the undergraduates at americas best institutions and 10 percent of all undergraduates in the uk. in the united states, 20 percent of the newly hired professors in science and engineering are foreign-born, and in china many newly hired faculty members at the top research universities received their graduate education abroad.universities are also encouraging students to spend some of their undergraduate years in another country. in europe, more than 140 000 students participate in the erasmus program each year, taking courses for credit in one of 2 200 participating institutions across the continent. and in the united states, institutions are helping place students in summer internships (实习) abroad to prepare them for global careers. yale and harvard have led the way, offering every undergraduate at least one international study or internship opportunity—and providing the financial resources to make it possible.globalization is also reshaping the way research is done. one new trend involves sourcing portions of a research program to another country. yale professor and howard hughes medical institute investigator tian xu directs a research centre focused on the genetics of human disease at shanghais fudan university, in collaboration with faculty colleagues from bothschools. the shanghai centre has 95 employees and graduate students working in a 4 300-square-meter laboratory facility. yale faculty, postdoctors and graduate students visit regularly and attend videoconference seminars with scientists from both campuses. thearrangement benefits both countries; xus yale lab is more productive, thanks to the lower costs of conducting research in china, and chinese graduate students, postdoctors and faculty get on-the-job training from a world-class scientist and his us team.as a result of its strength in science, the united states has consistently led the world in the commercialization of major new technologies, from the mainframe computer and the integrated circuit of the 1960s to the internet infrastructure (基础设施) and applications software of the 1990s. the link between university-based science and industrial application is often indirect but sometimes highly visible: silicon valley was intentionally created by stanford university, and route 128 outside boston has long housed companies spun off from mit and harvard. around the world, governments have encouraged copying of this model, perhaps most successfully in cambridge, england, where microsoft and scores of other leading software and biotechnology companies have set up shop around the university.for all its success, the united states remains deeply hesitant about sustaining the research-university model. most politicians recognize the link between investment in science and national economic strength, but support for research funding has been unsteady. the budget of the national institutes of health doubled between 1998 and 2003, but has risen more slowly than inflation since then. support for the physical sciences and engineering barely kept pace with inflation during that same period. the attempt to make up lost ground is welcome, but the nation would be better served by steady, predictable increases in science funding at the rate of long-term gdp growth, which is on the order of inflation plus 3 percent per year.american politicians have great difficulty recognizing that admitting more foreign students can greatly promote the national interest by increasing international understanding.adjusted for inflation, public funding for international exchanges and foreign-language study is well below the levels of 40 years ago. in the wake of september 11, changes in the visa process caused a dramatic decline in the number of foreign students seeking admission to us universities, and a corresponding surge in eollments in australia, singapore and the uk. objections from american university and business leaders led to improvements in the process and a reversal of the decline, but the united states is still seen by many as unwelcoming to international students.most americans recognize that universities contribute to the nations well-being through their scientific research, but many fear that foreign students threaten american competitiveness by taking their knowledge and skills back home. they fail to grasp that welcoming foreign students to the united states has two important positive effects: first, the very best of them stay in the states and—like immigrants throughout history—strengthen the nation; and second, foreign students who study in the united states become ambassadors for many of its most cherished (珍视) values when they return home. or at least they understand them better. in america as elsewhere, few instruments of foreign policy are as effective in promoting peace and stability as welcoming international university students.32. in the united states, how many of the newly hired professors in science and engineering are foreign-born? a. 10%. b. 20%. c. 30%. d. 38%.33. how do yale and harvard prepare their undergraduates for global careers? a. they organize a series of seminars on world economy. b. they offer them various courses in international politics. c. they arrange for them to participate in the erasmus program. d. they give them chances for international study or internship.34. an example illustrating the general trend of universities globalization is__________. a. yales collaboration with fudan university on genetic research b. yales helping chinese universities to launch research projects c. yales student exchange program with european institutions d. yales establishing branch campuses throughout the world 35. what do we learn about silicon valley from the passage? a. it housesmany companies spun off from mit and harvard. b. it is known to be the birthplace of microsoft company. c. it was intentionally created by stanford university. d. it is where the internet infrastructure was built up.第二节(共5小题;每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。
2016年(衡水金卷)普通高等学校招生全国统一考试模拟试题理综生物(五)—(全国卷I)第I卷(选择题)一、选择题(本题共13小题,每小题6分。
在每小题给出的四个选项中.只有一项是符合题目要求的)1.以下对垂体细胞的描述错误的是A.细胞中含量最多的有机物是蛋白质B.细胞膜上有甲状腺激素、胰岛素的受体C.细胞中不会含有麦芽糖、细胞分裂素D.细胞中RNA的种类和数量比DNA要少2.为了探究酵母菌的细胞呼吸类型,按装置1图示装配实验材料和用具,若想得到科学的实验结论,还必须设计装置2。
下列相关叙述,不正确的是A.装置2中甲是等量的酵母菌培养液,乙是等量的蒸馏水B.若装置1和2中红色液珠的移动方向相反,则酵母菌同时进行有氧呼吸和无氧呼吸C.若装置1中红色液珠左移,则细胞质基质和线粒体基质都能产生[H]和ATPD.降低实验温度,装置中红色液珠移动变慢是由于酵母菌内相关化学反应的活化能降低3.操纵基因是DNA分子上的一小段序列,它不编码任何蛋白质,但可与特定的阻遏蛋白结合,从而使RNA聚合酶不能与DNA相关序列接触而发挥作用,下列相关叙述错误的是A.操纵基因的基本组成单位是脱氧核糖核苷酸B.与阻遏蛋白结合后的操纵基因阻止了相关基因的转录C.RNA聚合酶在核糖体合成并主要运往细胞核发挥作用D.操纵基因编码的阻遏蛋白可抑制相关基因的表达4.小鼠骨骼肌细胞接受编码乙肝病毒(HBV)表面S蛋白的基因疫苗(需要运载体才能运入细胞)后,该基因可表达出S蛋白,而S蛋白可引起机体发生特异性免疫,如图甲所示。
图乙表示探究接种不同剂量的基因疫苗小鼠的抗体效价(一种衡量免疫效果的单位)的实验结果。
下列相关叙述,正确的是A.图甲中,树突状细胞能特异性识别不同的抗原B.图甲中,细抱④和⑥在二次免疫中发挥重要作用C.图乙中,对照组指的是不做任何处理的组别D.上述抗体效价实验,应随机挑选若干只小鼠,并均分成5组5.某草原生态系统中田鼠同化的能最包括①②③④四部分,其中①被转化成热能,②指未被利用的能量,③流向分解者,④流向下一营养级。
的菱形,则该棱柱的体积等于,则下列结论正确的是(卷(非选择题满足=+λ():极坐标与参数方程,,B,求点P到,A B两点的距离之积。
时,求此不等式的解集;若此不等式的解集为R次运(xb=-[a∵=(),·() ·=(-||+||)=0.安排在三个数学班中:有)中,由正弦定理得,中,由正弦定理得.=,得,整理得,所以,从=DE·=.取最小值.,又∵PQ 的中点在)4(2-=x y 上,∴⎪⎫⎛-+=+42n x m yee )(-=;∴∠ABC =∠AEG .∵∠ADC =180°-∠ABC =180°-∠AEG =∠CEF , ∴∠ADC +∠FDC =∠CEF +∠FDC =180°,∴C ,D ,F ,E 四点共圆. (2)由C ,D ,F ,E 四点共圆,知∠GCE =∠AFE ,∠GEC =∠GDF ,∴△GCE ∽△GFD ,故GC GF =GEGD ,即GC ·GD =GE ·GF .∵GH 为圆的切线,GCD 为割线,∴GH 2=GC ·GD ,∴GH 2=GE ·GF .23. 【答案】(1)1112x y t ⎧=⎪⎪⎨⎪=+⎪⎩(t 为参数) (2)2 【解析】(1)直线的参数方程为1cos 61sin 6x t y t ππ⎧=+⎪⎪⎨⎪=+⎪⎩,即12112x y t ⎧=+⎪⎪⎨⎪=+⎪⎩(t 为参数) (2)把直线12112x y t ⎧=+⎪⎪⎨⎪=+⎪⎩代入422=+y x ,得2221(1)(1)4,1)202t t t ++=+-= 122t t =-,则点P 到,A B 两点的距离之积为224. 【答案】(1){x|x≤0或x≥2}(2)[3,+∞)【解析】(1) 当a =1时,不等式为|x -1|≥1,∴ x≥2或x≤0,∴不等式解集为{x|x≤0或x≥2}. (2)不等式的解集为R ,即|ax -1|+|ax -a|≥2(a>0)恒成立.∵|ax -1|+|ax -a|= ∴ a =|a -1|≥2.∵a>0,∴ a≥3, ∴ 实数a 的取值范围为[3,+∞).。
金卷(十)2016年新课标I卷高考模拟试题文综政治卷12.2015年王先生按一年期存款基准利率1.5%,强1000元存入银行,在物价不变的情况下,到期获得利息可以购买15件A商品。
在其他条件不变的情况下,假定2016年银行存款基准利率不变,该商品的社会劳动生产率降低20%。
王先生10000元存款一年获得的利息,到期可以购买到A商品的数量为()A.18件B.12件C.18.75件D.20件13. 2015年以来,财政部关于环保节能减排的政策密集出台,中央财政加大节能减排支持力度,截至目前中央财政安排节能环保资金2000多亿元。
财政加大节能减排支持力度()①促进了资源的优化配置②扩大了国家财政赤字③促进国家经济平稳运行④促进产业的调整升级A.①②B.③④C.①④D.②③14.双十一是网购一族的狂欢日。
网购大军中,大学生是强大的一支,部分学生为了“任性”血拼,不仅办理了银行信用卡,还在网上注册了各类消费信贷平台账号,有学生每月的生活费几乎都用来还款。
材料学生的信贷消费()①违背了避免盲从、理性消费的原则②违背了量入为出,适度消费的原则③扩大了我国金融债券的发行量④增加了当前收入,提高了生活水平A.①②B.②③C.②④D.③④15.当前,我国农业资源环境遭受着外源性污染和源性污染的双重压力,农业已超过工业成为我国最大的面源污染产业,农业可持续发展遭受瓶颈。
在这一背景下,我国应()①把生态文明建设作为农业发展的首要任务②保护环境,推进绿色发展、循环发展、低碳发展③推动城乡发展一体化,走中国特色的农业现代化道路④加快转变农业发展方式,走可持续发展之路A.①②B.③④C.①④D.②③16.2015年市建立了人大代表基层联系点,每位市人大代表固定联系2名区人大代表和3名普通群众,经常性地开展调查研究,听取群众意见,并对环境等群众关心的问题,对政府提出质问。
人大代表基层联系点的建立()①创新了基层自治制度②完善了社情民意反映制度③贯彻了对人民负责的原则④贯彻了集中制的原则A.①②B.③④C.①③D.②④17.《刑法修正案(九〉》于2015年11月1日正式实施。
2016年普通高等学校招生全国统—考试模拟试题文科综合能力测试(一)地理测试题注意事项:1.本试卷分第I卷(选择题)和第Ⅱ卷(非选择题)两部分。
答卷前,考生务必将自己的姓名、准考证号填写在答题卡上。
2.回答第I卷时,将选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动,用橡皮擦干净后,再选涂其它答案标号。
写在本试卷上无效。
3.回答第Ⅱ卷时,将答案写在答题卡上。
写在本试卷上无效。
4.考试结束后,将本试卷和答题卡一并交回。
第I卷本卷共35个小题,每小题4分,共140分。
在每小题给出的四个选项中。
只有一项是符合题目要求的。
屋顶花园就是在屋顶上覆盖绿色植被,并配有排水设施,是以自然环境为依托,资源流动为命脉,社会环境为经络的半人工生态系统,具有降温隔热、美化环境、净化空气、降低噪音等功效。
下图示意屋顶花园结构。
据此完成l~3题。
1.设置排水层的目的是A.防止雨水聚积,达到快速排水目的B.储存全部雨水,为植物生长提供水分C.储存部分雨水,降低径流的洪峰值D.有效吸收和降解雨水的污染成分2.吸收城市噪音效果较好的层次是A.植被层和种植基质B.隔离过滤层和排水层C.保湿毯和根阻层D.防水层和结构层3.下列适合北京高层建筑屋顶绿化种植植物的品种是A.抗风、易倒伏、耐短时积水的植物B.阴性、耐贫瘠的浅根性植物C.尽量选用名贵品种,提高经济效益D.耐旱、抗寒性强的矮灌木和草本植物读2016年1月18日某地天气形势图,完成4~6题。
4.该日,札幌的天气状况最可能是A.大雪纷飞B.风和日丽C.电闪雷鸣D.寒冷干燥5.与图中航行高风险区成因最相似的地区是A.美国本土西海岸B.纽芬兰岛东部地区C.巴西东部沿海D.澳大利亚东部沿海6.若一架飞机从M地沿纬线向西飞行784千米,则飞机所到达地的经度大约是A.130°E B.133°E C.147°E D.150°E根据土地利用结构调整的需要。
数学(理)试题(五)第Ⅰ卷(共60分)一、选择题:本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的.1. 已知集合{}{}21,1,2,1,A B a a =-=-,若B A ⊆,则实数a 的不同取值个数为( )A .2B .3C .4D .5 2. 若()2211(i i z i -=+为虚数单位), 则复数z 的实部与虚部的和为( ) A .1 B .0 C .1- D .2 3. 下列函数中, 与函数()f x x =的单调性与奇偶性都相同的是( ) A .sin y x = B .3y x x =-C .2x y =D .(lg y x =4. 与双曲线2212x y -=有相同的渐近线, 且右焦点F 到渐近线的距离为2的双曲线方程是( )A .22146x y -= B .22136y x -= C .22184x y -= D .22148y x -= 5. 阅读如图所示的程序框图, 若输入的x 值为12-,则输出的y 值是( )46. 在第二届乌镇互联网大会中, 为了提高安保的级别同时又为了方便接待, 现将其中的五个参会国的人员按排酒店住宿, 这五个参会国要在a 、b 、c 三家酒店选择一家, 且这三家至少有一个参会国入住, 则这样的安排方法共有( )A .96种B .124种C .130种D .150种 7. 在各项均为正值的等比数列{}n a 中, 已知5a 、13a 分别是方程24220x mx e -+=的两根,则7911a a a 的值为( )A .6e BC .7e D .5e8. 已知某几何体的三视图如图所示, 则该几何体的表面积是( )A.8π+ B.38π+C.83π++ D.283π++ 9. 设点(),M x y 满足不等式组360200,0x y x y x y --≤⎧⎪-+≥⎨⎪≥≥⎩,点()11,0,0P a b a b ⎛⎫>> ⎪⎝⎭,当OP OM 最大时, 点M 为( )A .()0,2B .()0,0C .()4,6D .()2,0 10. 已知点O 是ABC ∆的外心, a 、b 、c 分别为角A 、B 、C 的对边, 若2220c c b -+=,则BC AO的最大值是( )12248611. 函数()1ln22016xx ef x e =的大致图象为( )A .B .C .D .12. 已知函数()x f x e ax =-的图象在区间()1,-+∞内与x 轴没有交点, 则实数a 的取值范围是( )A .1,e e ⎡⎫-⎪⎢⎣⎭B .1,e e ⎛⎫ ⎪⎝⎭C .11,e e ⎛⎫- ⎪⎝⎭D .()0,e第Ⅱ卷(共90分)二、填空题(每题5分,满分20分,将答案填在答题纸上)13. 若62a x x ⎛⎫- ⎪⎝⎭的展开式中常数项为160,则a 的值为 .14. 观察下列式子:222222*********11,11,11, (222332344)+<+++<++++<+,根据上述规律, 第n 个不等式应该为 .15. 将一个周长为18的矩形, 以一边为侧棱, 折成一个正三棱柱(底面为正三角形, 侧棱与底面垂直), 当这个正三棱柱的体积最大时, 它的外接球的半径为 . 16. 数列{}n a 满足121,2a a ==,且2121n n n a a a +--+=,则23111 (111)n a a a +++---的最小值为 .三、解答题 (本大题共6小题,共70分.解答应写出文字说明、证明过程或演算步骤.)17. (本小题满分12分)已知向量()3sin ,,cos ,14a x b x ⎛⎫==- ⎪⎝⎭.(1)当a b时, 求cos 2x 的值;(2)设函数()()2f x a b b =+,求当02x π≤≤时, 函数()f x 的最大值及对应的x 值. 18. (本小题满分12分)如图, 在四棱锥P ABCD -中, 底面ABCD 是边长为2的菱形, 且60DAB ∠= ,侧面PAD 为正三角形, 其所在平面垂直于底面,ABCD G 为AD 边的中点.(1)求证:平面PAD ⊥平面PGB ;(2)若点E 在BC 边上, 且14BE BC =,求平面PDC 和平面PGE 所成的锐二面角的余弦值.19. (本小题满分12分)从某企业生产某种产品中抽取100件, 测量这些产品的一项质量指标值, 由测量表得到如下频数分布表.(1)作出这些数据的频率分布直方图(用阴影表示) ;(2)统计方法中, 同一组数据常用该组区间的中点值作为代表, 据此估计这种产品质量指标值的平均数x 及方差2s ;(3) 当质量指标值位于()79.6,120.4时, 认为该产品为合格品, 由直方图可以认为, 这种产品的质量指标值Z 服从正态分布()2,N μσ,其中μ近似为样本平均数2,x σ近似为样本方差2s (每组数取中间值).①利用该正态分布, 求从该厂生产的产品中任取一件, 该产品为合格品的概率; ②该企业每年生产这种产品10万件, 生产一件合格品利润10元, 生产一件不合格品亏损20,则该企业的年利润是多少?(10.2≈,若()2,Z N μσ ,则()()0.6826,220.9544,P Z P Z μσμσμσμσ-<<+=-<<+=)20. (本小题满分12分)已知点()()121,0,1,0F F -,动点M 到点2F的距离是线段1MF 的中垂线交线段2MF 于点P .(1)当点M 变化时, 求动点P 的轨迹G 的方程;(2)直线l 与曲线G 相切于点N ,过2F 作2NF 的垂线与直线l 相交于点Q ,求证:Q 落在一条定直线m 上, 求直线m 的方程.21. (本小题满分12分)已知函数()ln 2f x x =+. (1)若()f x 的切线过()0,2P ,求此切线的方程;(2)若方程()()0f x kx k k =+>在区间[]1,e (其中e 为自然对数的底数) 内有实根, 求k 的取值范围.请考生在22、23、24三题中任选一题作答,如果多做,则按所做的第一题记分. 22.(本小题满分10分)选修4-1:几何证明选讲如图, 已知圆上的四点A 、B 、C 、,D CD AB ,过点D 的圆的切线DE 与BA 的延长线交于E 点.(1)求证:CDA EDB ∠=∠;(2)若5,7BC CD DE ===,求线段DE 的长.23. (本小题满分10分)选修4-4:坐标系与参数方程已知直线1cos 60:(sin 60x tl t y t⎧=+⎪⎨=⎪⎩为参数), 曲线cos :(sin x C y θθθ=⎧⎨=⎩为参数). (1)分别将直线l 和曲线C 的参数方程转化为普通方程; (2)求与直线l 平行且与曲线C 相切的直线2l 的方程.24. (本小题满分10分)选修4-5:不等式选讲 已知函数()1f x x a x =-++. (1)若2a =,求函数()f x 的最小值;(2)如果关于x 的不等式()2f x <的解集不是空集, 求实数a 的取值范围. 2016年(衡水金卷)普通高等学校招生全国统一模拟考试(全国卷I )数学(理)试题(五)参考答案一、选择题(每小题5分,共60分)1-5.ACDCB 6-10.DABCB 11-12.AA 二、填空题(每小题5分,共20分) 13.1- 14.()2221111...12311nn n ++++<+++15.616.1 三、解答题17.解:(1)由a b,可得2222222233cos sin 1tan 7cos sin 0,tan ,cos 2cos sin 44cos sin 1tan 25x x x x x x x x x x x x --+=∴=-∴=-===++.(2)()()21322sin cos 2cos 2242f x a b b x x x x π⎛⎫=+=++=++ ⎪⎝⎭.ABCD ,平面PAD 平面,ABCD AD BG =∴⊥平面PAD ,又BG ⊂平面,PGB ∴平面PAD ⊥平面PGB .(2)BG ⊥ 平面PAD ,,,BG AD BG PG PAD ∴⊥⊥∆ 是等边三角形, 且G 为AD 的中点,PG AD ∴⊥, 以G 为原点, 分别以GB 、GD 、GP 所在直线为x 轴、y 轴、z 轴, 建立如图所示的空间直角坐标系Gxyz .则())(())0,0,0,,,0,1,0,G BP D C,设E点坐标为)0,0,y 011,42BE BC y =∴= ,即((11,0,0,1,,,,,022E PD PC GP GE ⎫⎫∴====⎪⎪⎭⎭ ,设平面PDC 的一个法向量为(),,n x y z = ,则020n PD y y x z n PC y ⎧⎧===⎪⎪⇒⎨⎨=-⎪=+=⎪⎩⎩, ∴令1x =-,可得平面PDC的一个法向量为()n =-,设平面PGE 的一个法向量为(),,m a b c = ,则00102GP m c b GE m b ⎧===⎧⎪⎪⇒⎨⎨=-=+=⎪⎩⎪⎩,令1a =,得()1,m =-, cos ,m n m n m n∴=== ,∴平面PDC 与平面PGE 所成的锐二面角余19. 解:(1)由题意可得()10062622838x =-+++=,其频率分布直方图如图所示:(2)质量指标值的平均数为800.06900.261000.381100.221200.08100x =⨯+⨯+⨯+⨯+⨯=.质量指标值的方差为()()222222200.06100.2600.38100.22200.08104s =-⨯+-⨯+⨯+⨯+⨯=.(3) ①由(2) 可知Z 服从正态分布()100,104N ,从而()()79.6120.4100210,2100210.20.9544P Z P Z <<=-⨯<<+⨯=.②由①知, 一件产品为合格品的概率为0.9544,依题意()100000,0.9544X B ,所以()95440E X =,所以不合格品的件数为100000954404560-=,所以该企业的年利润为9544010456020863200⨯-⨯=(元).20. 解:(1)连接122,PF MF PM PF =∴+= ,又11212,2PM PF PF PF F F =∴+== ,由椭圆的定义可知动点P 的轨迹G 的方程为2212x y +=. (2)如图,当直线l 斜率不存在时, 不满足题意, 当直线l 斜率存在时, 设()00,N x y ,则220012x y +=,设直线()00:l y y k x x -=-,与椭圆2212x y +=联立, 得()220022x kx y kx ++-=⎡⎤⎣⎦,()()()()()()222222200000000124220,16412220k xk y kx x y kx k y kx k y kx ⎡⎤++-+--=∆=--+--=⎣⎦整理,得2002()120x k y k --=-,展开, 得22000202120()x k x k y y -+-=-,又220012x y +=,22200002202x y k kx y ∴---=,222000004x y k kx y ∴+-=,即20002x y k ⎛⎫+= ⎪⎝⎭,002x k y ∴=-, ∴直线()0000:2x l y x x y y =--+,① 直线0201:1x yQF x y -=--,② ①②联立, 消去y ,得()000000211x x x y y x x y --+-=--,同220022x y +=联立, 整理得()()0220x x --=,0020,2x x x ≤≤∴-≠∴= ,∴交点Q 的横坐标恒为2,即Q 点落在定直线2x =上.21. 解:(1)设切点为()()00011,ln 2,',x x f x k x x +==,∴切线方程为()()0001ln 2y x x x x -+=-,此直线过()0,2P ,代入得00ln 1,x x e =∴=,∴切线方程为()13y x e e -=-,即12y x e=+. (2)由()f x kx k =+,得[]()ln 21,1x k x e x +=∈+,设()()()21ln 1ln 2,'11x x x h x h x x x --+==++,设()()2111ln 1,'0x x x x x xϕϕ=--=--<,()x ϕ∴在区间[]1,e 内单调递减,∴ 当[]1,x e ∈时,()()()()10,'0,x h x h x ϕϕ≤=∴≤∴ 在区间[]1,e 内单调递减,()()()()min 3,max 111h x h e h x h e ====+, ∴当311k e ≤≤+时,()()0f x kx k k =+> 在区间[]1,e 内有实根,k ∴ 的取值范围是3,11e ⎡⎤⎢⎥+⎣⎦. 22. 解:(1),CD AB BDC ABD ∴∠=∠ ,又由DE 是圆的切线, 知,,ADE ABD ADE BDC CDA EDB ∠=∠∴∠=∠∴∠=∠.(2)在,BCD ADE ∆∆中,,,,,.BC CD AD BDC EDA BCD EAD BDC EDA BC EA ==∠=∠∠=∠∴∆∆≅∆∴= 又由切割线定理得,2DE EA EB = , 即49495,5BE BE =∴=.23. 解:(1)由题意可知,l 的普通方程为y C 的普通方程为221x y +=.(2)所求直线1l 0y c -+=,圆心到直线2l 的距离为12c d ==,所以2c =±,所以直线1l 20y -±=.24. 解:(1)当2a =时, 知()()()21213f x x x x x =-++≥--+=,当()()210x x -+≤,即12x -≤≤时取等号,()f x ∴ 的最小值是3.(2)()()()111f x x a x x a x a =-++≥--+=+ ,当()()10x a x -+≤时取等号,∴ 若关于x 的不等式()2f x <的解集不是空集, 只需12a +<,解得31a -<<,即实数a 的取值范围是()3,1-.。